Evaluate (x-4)^2+4=49

${(x - 4)}^{2} + 4 = 49$

Subtract $4$ from both sides of the equation.

${(x - 4)}^{2} = 49 - 4$

Subtract $4$ from $49$ .

${(x - 4)}^{2} = 45$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x - 4 = \pm \sqrt{45}$

Simplify $\pm \sqrt{45}$ .

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$x - 4 = \pm \sqrt{9 (5)}$

Rewrite $9$ as $3^{2}$ .

$x - 4 = \pm \sqrt{3^{2} \cdot 5}$

Pull terms out from under the radical.

$x - 4 = \pm 3 \sqrt{5}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x - 4 = 3 \sqrt{5}$

Add $4$ to both sides of the equation.

$x = 3 \sqrt{5} + 4$

Next, use the negative value of the $\pm$ to find the second solution.

$x - 4 = - 3 \sqrt{5}$

Add $4$ to both sides of the equation.

$x = - 3 \sqrt{5} + 4$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3 \sqrt{5} + 4, - 3 \sqrt{5} + 4$

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{5} + 4, - 3 \sqrt{5} + 4$

Decimal Form:

$x = 10.70820393 \dots, - 2.70820393 \dots$